{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4: Testing and regularization with Turi Create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining our dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Our original polynomial is -x^2+x+15\n",
    "coefs = [15,1,-1]\n",
    "\n",
    "def polynomial(coefs, x):\n",
    "    n = len(coefs)\n",
    "    return sum([coefs[i]*x**i for i in range(n)])\n",
    "\n",
    "def draw_polynomial(coefs):\n",
    "    n = len(coefs)\n",
    "    x = np.linspace(-5, 5, 1000)\n",
    "    plt.ylim(-20,20)\n",
    "    plt.plot(x, sum([coefs[i]*x**i for i in range(n)]), linestyle='-', color='black')\n",
    "\n",
    "draw_polynomial(coefs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = []\n",
    "Y = []\n",
    "for i in range(40):\n",
    "    x = random.uniform(-5,5)\n",
    "    y = polynomial(coefs, x) + random.gauss(0,2)\n",
    "    X.append(x)\n",
    "    Y.append(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a1ce3fb50>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y)\n",
    "#draw_polynomial(coefs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training a polynomial regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import turicreate as tc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">y</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.4442185152504816</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.685961311021467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.4108324970703663</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.690236225597948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.11274721368608542</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.205789026637378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.9668727392107255</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11.133217991032268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.23403045847644144</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.927272159051856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.046868558173902564</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.8584762866286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.1816215560029617</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.16012255928749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.4949365863755943</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.5061587527226514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.097462559682402</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.933186396721837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.021659504395828</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.454299054753137</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[40 rows x 2 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tx\tfloat\n",
       "\ty\tfloat\n",
       "\n",
       "Rows: 40\n",
       "\n",
       "Data:\n",
       "+----------------------+--------------------+\n",
       "|          x           |         y          |\n",
       "+----------------------+--------------------+\n",
       "|  3.4442185152504816  | 6.685961311021467  |\n",
       "| -2.4108324970703663  | 4.690236225597948  |\n",
       "| 0.11274721368608542  | 12.205789026637378 |\n",
       "| -1.9668727392107255  | 11.133217991032268 |\n",
       "| -0.23403045847644144 | 10.927272159051856 |\n",
       "| 0.046868558173902564 |  12.8584762866286  |\n",
       "| -2.1816215560029617  |  8.16012255928749  |\n",
       "| -2.4949365863755943  | 3.5061587527226514 |\n",
       "|  4.097462559682402   | 5.933186396721837  |\n",
       "|  4.021659504395828   | 2.454299054753137  |\n",
       "+----------------------+--------------------+\n",
       "[40 rows x 2 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = tc.SFrame({'x':X, 'y':Y})\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding columns to our dataset corresponding to $x^2, x^3, \\ldots, x^{200}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">y</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^2</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^3</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^4</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.4442185152504816</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.685961311021467</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11.862641180794233</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">40.85752839466433</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">140.72225578427518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.4108324970703663</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.690236225597948</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.812113328930538</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-14.012031690041567</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">33.78066134833202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.11274721368608542</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.205789026637378</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.012711934193975809</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0014332351609316464</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00016159327095197139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.9668727392107255</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11.133217991032268</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.8685883722503025</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-7.609021008606714</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">14.965975993910245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.23403045847644144</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.927272159051856</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.05477025549469338</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.012817908004294928</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0029997808869539904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.046868558173902564</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.8584762866286</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.002196661745300489</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0001029543687980023</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.82532282326659e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.1816215560029617</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.16012255928749</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.759472613616784</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-10.38336804907213</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">22.652579559768178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.4949365863755943</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.5061587527226514</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.224708570035504</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-15.530253150907287</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">38.74699678187344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.097462559682402</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.933186396721837</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">16.789199427999062</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">68.79311606326735</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">281.877217433124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.021659504395828</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.454299054753137</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">16.173745169297295</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">65.04529598178058</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">261.5900328013676</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^5</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^6</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^7</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^8</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">484.67819888001475</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1669.337626520802</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5749.563561467239</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19802.75327301497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-81.43951615108769</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">196.33703208272914</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-473.3356973233905</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1141.1330811306927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.821919105025542e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.054163026530763e-06</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.3160115769831987e-07</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.611238521695724e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-29.436170198104204</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">57.897200709418335</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-113.8764257519668</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">223.98043745029776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.0007020400963027086</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00016429876560656798</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.8450915442018495e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.998685369734469e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.2615592345012992e-07</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0599602054595068e-08</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.967880655160061e-10</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.328374034873745e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-49.419355866662336</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">107.81433204249198</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-235.21007082996135</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">513.1393607116271</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-96.67129988327346</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">241.1887629312657</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-601.7506688598845</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1501.329759614511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1154.9813448596813</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4732.492817694172</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19391.212134467747</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">79454.76570784066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1052.0260416708363</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4230.890529357441</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">17015.201109448648</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">68429.34526102059</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^9</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^10</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^11</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^12</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">68205.00947585523</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">234912.95646957512</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">809091.554144741</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2786688.1113181044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2751.0807154719087</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6632.394790923271</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-15989.59289535804</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">38548.230167054615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.9440986759096557e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.319389225257071e-10</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.7425188628734854e-11</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.219585739566023e-12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-440.5410165374837</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">866.4881159317581</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1704.2718540762376</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3352.0858499866713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.1059664627642036e-06</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.928602968167163e-07</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.1534432122885111e-07</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.6994084379841963e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0912753390408435e-12</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.114650171158102e-14</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.397162790860842e-15</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1235156371577601e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1119.475890562065</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2442.2727342758135</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5328.114842734408</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11623.930193768714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3745.7225454767195</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9345.340221121789</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-23316.03122980414</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">58172.019364314285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">325562.9276762143</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1333981.906973878</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5465940.919119198</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">22396488.26952693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">275199.526748567</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1106758.7923536084</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4451007.016342538</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">17900434.671406485</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^13</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^14</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^15</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^16</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9597962.78923021</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">33057481.14735185</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">113857188.63525297</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">392149037.191905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-92933.32599128349</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">224046.68236062035</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-540139.0226957856</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1302184.708850828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.757465350456092e-13</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.3639096247202026e-14</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.047658646511789e-15</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.818566617187669e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-6593.126277832797</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12967.840342043208</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-25506.091655201875</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">50167.236360426745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-6.317437943566161e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.4784728983292561e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.46007690240989e-10</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.097633838347318e-11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.265755799941768e-18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.467983820391356e-19</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1567084325826255e-20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.421325646274244e-22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-25359.01667619951</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">55323.77741983543</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-120695.54537862289</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">263312.00351153733</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-145135.49941537727</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">362103.8674733184</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-903426.1870272816</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2253991.0471041654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">91768772.1527527</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">376019108.04392916</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1540724216.9351716</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6313059793.687853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">71989453.22907849</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">289517068.79498243</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1164339071.404162</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4682575292.85196</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^17</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^18</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^19</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^20</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1350646974.634009</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4651923317.601501</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">16022240422.008537</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">55184097117.27649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3139349.2132856892</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7568445.103041429</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-18246253.406705353</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">43988660.66266614</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.687743874208667e-17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.667717013492988e-18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.77260942290812e-19</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.101834482875274e-19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-98672.56959886446</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">194076.38725187947</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-381723.5554102257</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">750801.6550509678</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.895092959762769e-11</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.4350947422875725e-12</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.0379472559240156e-12</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.4291127217826166e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.5408971643207432e-23</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1908818655987081e-24</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.581491599605866e-26</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.6159646373327602e-27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-574447.1428150975</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1253226.2695497284</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2734065.4441988654</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5964696.108587057</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5623564.728783217</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">14030437.387692597</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-35005051.56140628</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">87335383.84851664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">25867526141.672287</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">105991219877.10797</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">434295055101.5151</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1779507728133.6638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">18831723431.54716</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">75734779522.63525</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">304579495880.5286</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1224915024452.0178</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^21</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^22</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^23</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^24</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">190066089038.70444</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">654629142988.3524</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2254685814903.038</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7765630629761.665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-106049292.62815641</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">255667080.9592843</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-616370507.207763</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1485966049.0122192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.2422876788743593e-20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.4006447438963847e-21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.5791879223837807e-22</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.780490381354894e-23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1476731.3078740432</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2904542.5525964564</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5712865.566579505</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11236479.545680864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5.684863639697423e-14</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.3304312439744394e-14</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.113614339987204e-15</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.286805915060279e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.226064907857024e-28</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.746389445887741e-30</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.693249880344893e-31</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.2622873869380074e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-13012709.605500508</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">28388807.7773667</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-61933634.99632773</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">135115753.149608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-217896244.44882032</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">543637312.3092018</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1356340620.199123</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3383983836.9221563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7291466290693.178</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">29876510131301.617</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">122417881676980.34</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">501602686807057.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4926191150164.705</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">19811463459530.504</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">79674960318011.5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">320425561425291.4</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^25</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^26</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^27</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^28</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">26746528797621.383</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">92120889703447.77</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">317284473957962.25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1092797059807522.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3582415240.501915</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8636603079.802168</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-20821403369.085075</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">50196915876.80071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.0074532949263996e-24</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.2633476560790303e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.5518614182584302e-26</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.8771526462166026e-27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-22100725.30309861</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">43469314.115449354</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-85498608.92586532</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">168164883.1367233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.7053345291304025e-16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.991002217080945e-17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-9.340160786439478e-18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.1858821110941107e-18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.916158982688746e-34</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.772818414462037e-35</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.2995800116388224e-36</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.090944137713512e-38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-294771439.6267598</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">643079726.7837648</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1402956594.1799567</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3060720347.9994926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-8442825082.440751</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">21064313190.550972</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-52554125645.979645</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">131119210839.13454</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2055298229028015.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8421507542423838.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.450681185116463e+16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.4139036961415208e+17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1288642504557392.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5182481376221680.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.084217548303629e+16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.38201331236386e+16</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^29</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^30</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^31</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^32</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3763831866800358.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.2963459403923578e+16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.464898690069156e+16</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.5378086737053808e+17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-121016356048.49858</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">291750163838.75836</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-703360776008.0823</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1695685015964.9155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.243909442104694e-28</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.657417510472881e-29</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.123636335925165e-30</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.649285071302609e-31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-330758924.3341785</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">650560711.5235589</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1279570128.6972206</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2516751604.042923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5.115629926348064e-19</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1972132170590418e-19</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.80184358082383e-20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.557167377994753e-21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.8547376965241654e-39</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.3379743980077544e-40</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.270893090821871e-42</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.939077176295085e-43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-6677333488.09258</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">14567414674.243217</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-31780585868.562866</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">69333211193.25986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-327134116299.25214</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">816178875406.6528</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2036314537278.946</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5080475640425.731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.793417457936445e+17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.373831112650498e+18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.726684107094634e+18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.985472395867812e+19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.3709603503640474e+17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.355685473198306e+18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.452105368259323e+18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.1926511373227622e+19</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^33</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^34</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^35</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^36</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.2965491068888595e+17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.824247250088001e+18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.283106155147869e+18</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.164039055284456e+19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4088012541283.5015</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9855513482957.477</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-23759992180029.04</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">57281361277751.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.241939374216821e-32</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.910140587543289e-33</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.663518837385496e-34</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.512931822599581e-35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4950130121.356891</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9736275991.242748</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-19150015828.607246</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">37665644088.741486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.5345768877788774e-21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.591377326142413e-22</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-8.404916821990053e-23</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.967006537306687e-23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.3775030961477547e-44</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.456158399653193e-46</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.0259083553407537e-47</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.4181996178118595e-48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-151258828086.12152</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">329989519888.4289</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-719912249843.6646</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1570576082689.5286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-12675464551488.137</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">31624480258814.664</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-78901072822829.44</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">196853173289962.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.6330323924716077e+20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.691289086900991e+20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.741730650958826e+21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1234138691037448e+22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.818096286238407e+19</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.5463380740228245e+20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.4262164221194687e+21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.735756829342173e+21</td>\n",
       "    </tr>\n",
       "</table>\n",
       "<table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^37</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^38</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x^39</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">...</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.453423381935882e+19</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.567121881406443e+20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.841728714844722e+20</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-138095767244832.11</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">332925763381706.7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-802628249472577.9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">8.470621296116262e-36</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.55038949327126e-37</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0767798049831999e-37</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-74083528562.95924</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">145712872755.02365</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-286598677173.93726</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.603394417520415e-24</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0773345060801938e-24</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-2.521290883904383e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.646897128962152e-50</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.115304847647085e-51</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.460098464813881e-52</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3426402637338.1655</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7475113853162.34</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-16307869515635.318</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-491136184185261.7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1225353634816712.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3057179614752534.0</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.603146267680541e+22</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.8861219488562804e+23</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.728314068433815e+23</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.306726096762723e+22</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.276866931083695e+22</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.7308400064408095e+23</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">...</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[40 rows x 200 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tx\tfloat\n",
       "\ty\tfloat\n",
       "\tx^2\tfloat\n",
       "\tx^3\tfloat\n",
       "\tx^4\tfloat\n",
       "\tx^5\tfloat\n",
       "\tx^6\tfloat\n",
       "\tx^7\tfloat\n",
       "\tx^8\tfloat\n",
       "\tx^9\tfloat\n",
       "\tx^10\tfloat\n",
       "\tx^11\tfloat\n",
       "\tx^12\tfloat\n",
       "\tx^13\tfloat\n",
       "\tx^14\tfloat\n",
       "\tx^15\tfloat\n",
       "\tx^16\tfloat\n",
       "\tx^17\tfloat\n",
       "\tx^18\tfloat\n",
       "\tx^19\tfloat\n",
       "\tx^20\tfloat\n",
       "\tx^21\tfloat\n",
       "\tx^22\tfloat\n",
       "\tx^23\tfloat\n",
       "\tx^24\tfloat\n",
       "\tx^25\tfloat\n",
       "\tx^26\tfloat\n",
       "\tx^27\tfloat\n",
       "\tx^28\tfloat\n",
       "\tx^29\tfloat\n",
       "\tx^30\tfloat\n",
       "\tx^31\tfloat\n",
       "\tx^32\tfloat\n",
       "\tx^33\tfloat\n",
       "\tx^34\tfloat\n",
       "\tx^35\tfloat\n",
       "\tx^36\tfloat\n",
       "\tx^37\tfloat\n",
       "\tx^38\tfloat\n",
       "\tx^39\tfloat\n",
       "\tx^40\tfloat\n",
       "\tx^41\tfloat\n",
       "\tx^42\tfloat\n",
       "\tx^43\tfloat\n",
       "\tx^44\tfloat\n",
       "\tx^45\tfloat\n",
       "\tx^46\tfloat\n",
       "\tx^47\tfloat\n",
       "\tx^48\tfloat\n",
       "\tx^49\tfloat\n",
       "\tx^50\tfloat\n",
       "\tx^51\tfloat\n",
       "\tx^52\tfloat\n",
       "\tx^53\tfloat\n",
       "\tx^54\tfloat\n",
       "\tx^55\tfloat\n",
       "\tx^56\tfloat\n",
       "\tx^57\tfloat\n",
       "\tx^58\tfloat\n",
       "\tx^59\tfloat\n",
       "\tx^60\tfloat\n",
       "\tx^61\tfloat\n",
       "\tx^62\tfloat\n",
       "\tx^63\tfloat\n",
       "\tx^64\tfloat\n",
       "\tx^65\tfloat\n",
       "\tx^66\tfloat\n",
       "\tx^67\tfloat\n",
       "\tx^68\tfloat\n",
       "\tx^69\tfloat\n",
       "\tx^70\tfloat\n",
       "\tx^71\tfloat\n",
       "\tx^72\tfloat\n",
       "\tx^73\tfloat\n",
       "\tx^74\tfloat\n",
       "\tx^75\tfloat\n",
       "\tx^76\tfloat\n",
       "\tx^77\tfloat\n",
       "\tx^78\tfloat\n",
       "\tx^79\tfloat\n",
       "\tx^80\tfloat\n",
       "\tx^81\tfloat\n",
       "\tx^82\tfloat\n",
       "\tx^83\tfloat\n",
       "\tx^84\tfloat\n",
       "\tx^85\tfloat\n",
       "\tx^86\tfloat\n",
       "\tx^87\tfloat\n",
       "\tx^88\tfloat\n",
       "\tx^89\tfloat\n",
       "\tx^90\tfloat\n",
       "\tx^91\tfloat\n",
       "\tx^92\tfloat\n",
       "\tx^93\tfloat\n",
       "\tx^94\tfloat\n",
       "\tx^95\tfloat\n",
       "\tx^96\tfloat\n",
       "\tx^97\tfloat\n",
       "\tx^98\tfloat\n",
       "\tx^99\tfloat\n",
       "\tx^100\tfloat\n",
       "\tx^101\tfloat\n",
       "\tx^102\tfloat\n",
       "\tx^103\tfloat\n",
       "\tx^104\tfloat\n",
       "\tx^105\tfloat\n",
       "\tx^106\tfloat\n",
       "\tx^107\tfloat\n",
       "\tx^108\tfloat\n",
       "\tx^109\tfloat\n",
       "\tx^110\tfloat\n",
       "\tx^111\tfloat\n",
       "\tx^112\tfloat\n",
       "\tx^113\tfloat\n",
       "\tx^114\tfloat\n",
       "\tx^115\tfloat\n",
       "\tx^116\tfloat\n",
       "\tx^117\tfloat\n",
       "\tx^118\tfloat\n",
       "\tx^119\tfloat\n",
       "\tx^120\tfloat\n",
       "\tx^121\tfloat\n",
       "\tx^122\tfloat\n",
       "\tx^123\tfloat\n",
       "\tx^124\tfloat\n",
       "\tx^125\tfloat\n",
       "\tx^126\tfloat\n",
       "\tx^127\tfloat\n",
       "\tx^128\tfloat\n",
       "\tx^129\tfloat\n",
       "\tx^130\tfloat\n",
       "\tx^131\tfloat\n",
       "\tx^132\tfloat\n",
       "\tx^133\tfloat\n",
       "\tx^134\tfloat\n",
       "\tx^135\tfloat\n",
       "\tx^136\tfloat\n",
       "\tx^137\tfloat\n",
       "\tx^138\tfloat\n",
       "\tx^139\tfloat\n",
       "\tx^140\tfloat\n",
       "\tx^141\tfloat\n",
       "\tx^142\tfloat\n",
       "\tx^143\tfloat\n",
       "\tx^144\tfloat\n",
       "\tx^145\tfloat\n",
       "\tx^146\tfloat\n",
       "\tx^147\tfloat\n",
       "\tx^148\tfloat\n",
       "\tx^149\tfloat\n",
       "\tx^150\tfloat\n",
       "\tx^151\tfloat\n",
       "\tx^152\tfloat\n",
       "\tx^153\tfloat\n",
       "\tx^154\tfloat\n",
       "\tx^155\tfloat\n",
       "\tx^156\tfloat\n",
       "\tx^157\tfloat\n",
       "\tx^158\tfloat\n",
       "\tx^159\tfloat\n",
       "\tx^160\tfloat\n",
       "\tx^161\tfloat\n",
       "\tx^162\tfloat\n",
       "\tx^163\tfloat\n",
       "\tx^164\tfloat\n",
       "\tx^165\tfloat\n",
       "\tx^166\tfloat\n",
       "\tx^167\tfloat\n",
       "\tx^168\tfloat\n",
       "\tx^169\tfloat\n",
       "\tx^170\tfloat\n",
       "\tx^171\tfloat\n",
       "\tx^172\tfloat\n",
       "\tx^173\tfloat\n",
       "\tx^174\tfloat\n",
       "\tx^175\tfloat\n",
       "\tx^176\tfloat\n",
       "\tx^177\tfloat\n",
       "\tx^178\tfloat\n",
       "\tx^179\tfloat\n",
       "\tx^180\tfloat\n",
       "\tx^181\tfloat\n",
       "\tx^182\tfloat\n",
       "\tx^183\tfloat\n",
       "\tx^184\tfloat\n",
       "\tx^185\tfloat\n",
       "\tx^186\tfloat\n",
       "\tx^187\tfloat\n",
       "\tx^188\tfloat\n",
       "\tx^189\tfloat\n",
       "\tx^190\tfloat\n",
       "\tx^191\tfloat\n",
       "\tx^192\tfloat\n",
       "\tx^193\tfloat\n",
       "\tx^194\tfloat\n",
       "\tx^195\tfloat\n",
       "\tx^196\tfloat\n",
       "\tx^197\tfloat\n",
       "\tx^198\tfloat\n",
       "\tx^199\tfloat\n",
       "\n",
       "Rows: 40\n",
       "\n",
       "Data:\n",
       "+----------------------+--------------------+----------------------+\n",
       "|          x           |         y          |         x^2          |\n",
       "+----------------------+--------------------+----------------------+\n",
       "|  3.4442185152504816  | 6.685961311021467  |  11.862641180794233  |\n",
       "| -2.4108324970703663  | 4.690236225597948  |  5.812113328930538   |\n",
       "| 0.11274721368608542  | 12.205789026637378 | 0.012711934193975809 |\n",
       "| -1.9668727392107255  | 11.133217991032268 |  3.8685883722503025  |\n",
       "| -0.23403045847644144 | 10.927272159051856 | 0.05477025549469338  |\n",
       "| 0.046868558173902564 |  12.8584762866286  | 0.002196661745300489 |\n",
       "| -2.1816215560029617  |  8.16012255928749  |  4.759472613616784   |\n",
       "| -2.4949365863755943  | 3.5061587527226514 |  6.224708570035504   |\n",
       "|  4.097462559682402   | 5.933186396721837  |  16.789199427999062  |\n",
       "|  4.021659504395828   | 2.454299054753137  |  16.173745169297295  |\n",
       "+----------------------+--------------------+----------------------+\n",
       "+-----------------------+------------------------+------------------------+\n",
       "|          x^3          |          x^4           |          x^5           |\n",
       "+-----------------------+------------------------+------------------------+\n",
       "|   40.85752839466433   |   140.72225578427518   |   484.67819888001475   |\n",
       "|  -14.012031690041567  |   33.78066134833202    |   -81.43951615108769   |\n",
       "| 0.0014332351609316464 | 0.00016159327095197139 | 1.821919105025542e-05  |\n",
       "|   -7.609021008606714  |   14.965975993910245   |  -29.436170198104204   |\n",
       "| -0.012817908004294928 | 0.0029997808869539904  | -0.0007020400963027086 |\n",
       "| 0.0001029543687980023 |  4.82532282326659e-06  | 2.2615592345012992e-07 |\n",
       "|   -10.38336804907213  |   22.652579559768178   |  -49.419355866662336   |\n",
       "|  -15.530253150907287  |   38.74699678187344    |   -96.67129988327346   |\n",
       "|   68.79311606326735   |    281.877217433124    |   1154.9813448596813   |\n",
       "|   65.04529598178058   |   261.5900328013676    |   1052.0260416708363   |\n",
       "+-----------------------+------------------------+------------------------+\n",
       "+------------------------+-------------------------+-----------------------+\n",
       "|          x^6           |           x^7           |          x^8          |\n",
       "+------------------------+-------------------------+-----------------------+\n",
       "|   1669.337626520802    |    5749.563561467239    |   19802.75327301497   |\n",
       "|   196.33703208272914   |    -473.3356973233905   |   1141.1330811306927  |\n",
       "| 2.054163026530763e-06  |  2.3160115769831987e-07 | 2.611238521695724e-08 |\n",
       "|   57.897200709418335   |    -113.8764257519668   |   223.98043745029776  |\n",
       "| 0.00016429876560656798 | -3.8450915442018495e-05 | 8.998685369734469e-06 |\n",
       "| 1.0599602054595068e-08 |  4.967880655160061e-10  | 2.328374034873745e-11 |\n",
       "|   107.81433204249198   |   -235.21007082996135   |   513.1393607116271   |\n",
       "|   241.1887629312657    |    -601.7506688598845   |   1501.329759614511   |\n",
       "|   4732.492817694172    |    19391.212134467747   |   79454.76570784066   |\n",
       "|   4230.890529357441    |    17015.201109448648   |   68429.34526102059   |\n",
       "+------------------------+-------------------------+-----------------------+\n",
       "+-------------------------+-----------------------+-------------------------+\n",
       "|           x^9           |          x^10         |           x^11          |\n",
       "+-------------------------+-----------------------+-------------------------+\n",
       "|    68205.00947585523    |   234912.95646957512  |     809091.554144741    |\n",
       "|   -2751.0807154719087   |   6632.394790923271   |    -15989.59289535804   |\n",
       "|  2.9440986759096557e-09 | 3.319389225257071e-10 |  3.7425188628734854e-11 |\n",
       "|    -440.5410165374837   |   866.4881159317581   |   -1704.2718540762376   |\n",
       "| -2.1059664627642036e-06 | 4.928602968167163e-07 | -1.1534432122885111e-07 |\n",
       "|  1.0912753390408435e-12 | 5.114650171158102e-14 |  2.397162790860842e-15  |\n",
       "|    -1119.475890562065   |   2442.2727342758135  |    -5328.114842734408   |\n",
       "|   -3745.7225454767195   |   9345.340221121789   |    -23316.03122980414   |\n",
       "|    325562.9276762143    |   1333981.906973878   |    5465940.919119198    |\n",
       "|     275199.526748567    |   1106758.7923536084  |    4451007.016342538    |\n",
       "+-------------------------+-----------------------+-------------------------+\n",
       "+------------------------+------------------------+------------------------+\n",
       "|          x^12          |          x^13          |          x^14          |\n",
       "+------------------------+------------------------+------------------------+\n",
       "|   2786688.1113181044   |    9597962.78923021    |   33057481.14735185    |\n",
       "|   38548.230167054615   |   -92933.32599128349   |   224046.68236062035   |\n",
       "| 4.219585739566023e-12  | 4.757465350456092e-13  | 5.3639096247202026e-14 |\n",
       "|   3352.0858499866713   |   -6593.126277832797   |   12967.840342043208   |\n",
       "| 2.6994084379841963e-08 | -6.317437943566161e-09 | 1.4784728983292561e-09 |\n",
       "| 1.1235156371577601e-16 | 5.265755799941768e-18  | 2.467983820391356e-19  |\n",
       "|   11623.930193768714   |   -25359.01667619951   |   55323.77741983543    |\n",
       "|   58172.019364314285   |  -145135.49941537727   |   362103.8674733184    |\n",
       "|   22396488.26952693    |    91768772.1527527    |   376019108.04392916   |\n",
       "|   17900434.671406485   |   71989453.22907849    |   289517068.79498243   |\n",
       "+------------------------+------------------------+------------------------+\n",
       "+------------------------+-----------------------+------------------------+\n",
       "|          x^15          |          x^16         |          x^17          |\n",
       "+------------------------+-----------------------+------------------------+\n",
       "|   113857188.63525297   |    392149037.191905   |   1350646974.634009    |\n",
       "|   -540139.0226957856   |   1302184.708850828   |  -3139349.2132856892   |\n",
       "| 6.047658646511789e-15  | 6.818566617187669e-16 | 7.687743874208667e-17  |\n",
       "|  -25506.091655201875   |   50167.236360426745  |   -98672.56959886446   |\n",
       "| -3.46007690240989e-10  | 8.097633838347318e-11 | -1.895092959762769e-11 |\n",
       "| 1.1567084325826255e-20 | 5.421325646274244e-22 | 2.5408971643207432e-23 |\n",
       "|  -120695.54537862289   |   263312.00351153733  |   -574447.1428150975   |\n",
       "|   -903426.1870272816   |   2253991.0471041654  |   -5623564.728783217   |\n",
       "|   1540724216.9351716   |   6313059793.687853   |   25867526141.672287   |\n",
       "|   1164339071.404162    |    4682575292.85196   |   18831723431.54716    |\n",
       "+------------------------+-----------------------+------------------------+\n",
       "+------------------------+-------------------------+-----+\n",
       "|          x^18          |           x^19          | ... |\n",
       "+------------------------+-------------------------+-----+\n",
       "|   4651923317.601501    |    16022240422.008537   | ... |\n",
       "|   7568445.103041429    |   -18246253.406705353   | ... |\n",
       "| 8.667717013492988e-18  |   9.77260942290812e-19  | ... |\n",
       "|   194076.38725187947   |    -381723.5554102257   | ... |\n",
       "| 4.4350947422875725e-12 | -1.0379472559240156e-12 | ... |\n",
       "| 1.1908818655987081e-24 |  5.581491599605866e-26  | ... |\n",
       "|   1253226.2695497284   |   -2734065.4441988654   | ... |\n",
       "|   14030437.387692597   |    -35005051.56140628   | ... |\n",
       "|   105991219877.10797   |    434295055101.5151    | ... |\n",
       "|   75734779522.63525    |    304579495880.5286    | ... |\n",
       "+------------------------+-------------------------+-----+\n",
       "[40 rows x 200 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(2,200):\n",
    "    string = 'x^'+str(i)\n",
    "    data[string] = data['x'].apply(lambda x:x**i)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting data into training and testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "train, test = data.random_split(.8, seed=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def display_results(model):\n",
    "    coefs = model.coefficients\n",
    "    print(\"Training error (rmse):\", model.evaluate(train)['rmse'])\n",
    "    print(\"Testing error (rmse):\", model.evaluate(test)['rmse'])\n",
    "    plt.scatter(train['x'], train['y'], marker='o')\n",
    "    plt.scatter(test['x'], test['y'], marker='^')\n",
    "    draw_polynomial(coefs['value'])\n",
    "    plt.show()\n",
    "    print(\"Polynomial coefficients\")\n",
    "    print(coefs['name', 'value'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training a polynomial regression model with no regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_no_reg = tc.linear_regression.create(\n",
    "    train, target='y', l1_penalty=0.0, l2_penalty=0.0, verbose=False, validation_set=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training error (rmse): 1.5213829303807986\n",
      "Testing error (rmse): 699.0325176744669\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial coefficients\n",
      "+-------------+---------------------+\n",
      "|     name    |        value        |\n",
      "+-------------+---------------------+\n",
      "| (intercept) |  8.409132643442717  |\n",
      "|      x      |  15.877898056607998 |\n",
      "|     x^2     |  108.8735358163443  |\n",
      "|     x^3     | -212.88678661687192 |\n",
      "|     x^4     |  -97.13225053973962 |\n",
      "|     x^5     |  258.47096686275455 |\n",
      "|     x^6     |  38.335889248828835 |\n",
      "|     x^7     | -128.78387647931117 |\n",
      "|     x^8     |  -9.214500432847792 |\n",
      "|     x^9     |  32.840417055946915 |\n",
      "+-------------+---------------------+\n",
      "[200 rows x 2 columns]\n",
      "Note: Only the head of the SFrame is printed.\n",
      "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n"
     ]
    }
   ],
   "source": [
    "display_results(model_no_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training a polynomial regression model with L1 regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_L1_reg = tc.linear_regression.create(\n",
    "    train, target='y', l1_penalty=0.1, l2_penalty=0.0, verbose=False, validation_set=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training error (rmse): 9.473874911154354\n",
      "Testing error (rmse): 10.077027617091746\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial coefficients\n",
      "+-------------+-------------------------+\n",
      "|     name    |          value          |\n",
      "+-------------+-------------------------+\n",
      "| (intercept) |    0.5655798426406278   |\n",
      "|      x      |    0.0694081636504658   |\n",
      "|     x^2     |  0.0075528368273853445  |\n",
      "|     x^3     |   0.003947237269580271  |\n",
      "|     x^4     | -0.00021279451431743294 |\n",
      "|     x^5     |  0.00019048017792383447 |\n",
      "|     x^6     |  -1.798514046251732e-05 |\n",
      "|     x^7     |   7.88081493506395e-06  |\n",
      "|     x^8     |  -8.895545466589715e-07 |\n",
      "|     x^9     |  3.020651102542037e-07  |\n",
      "+-------------+-------------------------+\n",
      "[200 rows x 2 columns]\n",
      "Note: Only the head of the SFrame is printed.\n",
      "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n"
     ]
    }
   ],
   "source": [
    "display_results(model_L1_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training a polynomial regression model with L2 regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_L2_reg = tc.linear_regression.create(\n",
    "    train, target='y', l1_penalty=0.0, l2_penalty=0.1, verbose=False, validation_set=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training error (rmse): 1.714673638689723\n",
      "Testing error (rmse): 3.413615797210576\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial coefficients\n",
      "+-------------+-------------------------+\n",
      "|     name    |          value          |\n",
      "+-------------+-------------------------+\n",
      "| (intercept) |    13.242877632262703   |\n",
      "|      x      |    0.8742327276128922   |\n",
      "|     x^2     |    -0.519442544052024   |\n",
      "|     x^3     |   0.006007308646500496  |\n",
      "|     x^4     |  -0.021611699669646676  |\n",
      "|     x^5     |  0.0011472313840807627  |\n",
      "|     x^6     | -0.00039568239266103136 |\n",
      "|     x^7     |  3.537559873068439e-05  |\n",
      "|     x^8     |  -1.065260727829058e-07 |\n",
      "|     x^9     |  5.825198471939245e-07  |\n",
      "+-------------+-------------------------+\n",
      "[200 rows x 2 columns]\n",
      "Note: Only the head of the SFrame is printed.\n",
      "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n"
     ]
    }
   ],
   "source": [
    "display_results(model_L2_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Viewing the predictions in the testing set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = test['x', 'y']\n",
    "predictions['No reg'] = model_no_reg.predict(test)\n",
    "predictions['L1 reg'] = model_L1_reg.predict(test)\n",
    "predictions['L2 reg'] = model_L2_reg.predict(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">x</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">y</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">No reg</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">L1 reg</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">L2 reg</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.2785728454728664</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">16.36505651355184</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">16.052528555808884</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.5467437924583818</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.958767791803519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.6530992777164</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4.83366913200435</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1499.3940900560701</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.230320283464282</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">6.450393351997895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.5203042856442961</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">13.47860807272069</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">44.58735982592923</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.5309318651483861</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">12.644906915280373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.14466863291336</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.2664703661537313</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-819.6674023489759</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.0254405801644775</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.08207753278438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-1.1509885402733957</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">13.436894195835205</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">79.74336216300665</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.4888537292170774</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">11.498079646733478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.424602231401824</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.5269925176080537</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-121.30631289217854</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.1270992482748206</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.701281752205773</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[6 rows x 5 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tx\tfloat\n",
       "\ty\tfloat\n",
       "\tNo reg\tfloat\n",
       "\tL1 reg\tfloat\n",
       "\tL2 reg\tfloat\n",
       "\n",
       "Rows: 6\n",
       "\n",
       "Data:\n",
       "+---------------------+--------------------+---------------------+\n",
       "|          x          |         y          |        No reg       |\n",
       "+---------------------+--------------------+---------------------+\n",
       "| -0.2785728454728664 | 16.36505651355184  |  16.052528555808884 |\n",
       "|   3.6530992777164   |  4.83366913200435  |  1499.3940900560701 |\n",
       "| -0.5203042856442961 | 13.47860807272069  |  44.58735982592923  |\n",
       "|   3.14466863291336  | 3.2664703661537313 |  -819.6674023489759 |\n",
       "| -1.1509885402733957 | 13.436894195835205 |  79.74336216300665  |\n",
       "|  3.424602231401824  | 3.5269925176080537 | -121.30631289217854 |\n",
       "+---------------------+--------------------+---------------------+\n",
       "+--------------------+--------------------+\n",
       "|       L1 reg       |       L2 reg       |\n",
       "+--------------------+--------------------+\n",
       "| 0.5467437924583818 | 12.958767791803519 |\n",
       "| 1.230320283464282  | 6.450393351997895  |\n",
       "| 0.5309318651483861 | 12.644906915280373 |\n",
       "| 1.0254405801644775 |  9.08207753278438  |\n",
       "| 0.4888537292170774 | 11.498079646733478 |\n",
       "| 1.1270992482748206 | 7.701281752205773  |\n",
       "+--------------------+--------------------+\n",
       "[6 rows x 5 columns]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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